-
1
-
-
84914830669
-
p bounds of solutions to reaction-diffusion equations
-
p bounds of solutions to reaction-diffusion equations, Commun. Part. Diff. Eqn., 4, 827-868, 1979.
-
(1979)
Commun. Part. Diff. Eqn.
, vol.4
, pp. 827-868
-
-
Alikakos, N.D.1
-
2
-
-
31744443874
-
-
Lectures in Mathematics, Birkhäuser
-
L.A. Ambrosio, N. Gigli, and G. Savaŕe, Gradient Flows in Metric Spaces and in the Space of Probability Measures, Lectures in Mathematics, Birkhäuser, 2005.
-
(2005)
Gradient Flows in Metric Spaces and in the Space of Probability Measures
-
-
Ambrosio, L.A.1
Gigli, N.2
Savaŕe, G.3
-
3
-
-
85038487574
-
Global minimizers for free energies of subcritical aggregation equations with degenerate diffusion
-
J. Bedrossian, Global minimizers for free energies of subcritical aggregation equations with degenerate diffusion, Appl. Math. Lett., to appear.
-
Appl. Math. Lett., to appear
-
-
Bedrossian, J.1
-
4
-
-
79961212313
-
Part I: A Virtual Node Method for Elliptic Interface Problems. Part II: Local and Global Theory of Aggregation Equations with Nonlinear Diffusion
-
PhD thesis, UCLA
-
J. Bedrossian, Part I: A Virtual Node Method for Elliptic Interface Problems. Part II: Local and Global Theory of Aggregation Equations with Nonlinear Diffusion, PhD thesis, UCLA, 2011.
-
(2011)
-
-
Bedrossian, J.1
-
5
-
-
79957801928
-
Local and global well-posedness for aggregation equations and Patlak-Keller-Segel models with degenerate diffusion
-
J. Bedrossian, N. Rodríguez, and A.L. Bertozzi, Local and global well-posedness for aggregation equations and Patlak-Keller-Segel models with degenerate diffusion, Nonlinearity, 24(6), 1683-1714, 2011.
-
(2011)
Nonlinearity
, vol.24
, Issue.6
, pp. 1683-1714
-
-
Bedrossian, J.1
Rodríguez, N.2
Bertozzi, A.L.3
-
6
-
-
79953065830
-
Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion
-
A.L. Bertozzi and D. Slepčev, Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion, Commun. Pure. Appl. Anal., 9(6), 1617-1637, 2010.
-
(2010)
Commun. Pure. Appl. Anal.
, vol.9
, Issue.6
, pp. 1617-1637
-
-
Bertozzi, A.L.1
Slepčev, D.2
-
8
-
-
60449088258
-
Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
-
A. Blanchet, J.A. Carrillo, and P. Laurencot, Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions, Calc. Var., 35, 133-168, 2009.
-
(2009)
Calc. Var.
, vol.35
, pp. 133-168
-
-
Blanchet, A.1
Carrillo, J.A.2
Laurencot, P.3
-
9
-
-
70349981450
-
Asymptotic behavior for small mass in the two-dimensional parabolic-elliptic Keller-Segel model
-
A. Blanchet, J. Dolbeault, M. Escobedo, and J. Fernández, Asymptotic behavior for small mass in the two-dimensional parabolic-elliptic Keller-Segel model, J. Math. Anal. Appl., 361, 533-542, 2010.
-
(2010)
J. Math. Anal. Appl.
, vol.361
, pp. 533-542
-
-
Blanchet, A.1
Dolbeault, J.2
Escobedo, M.3
Fernández, J.4
-
10
-
-
33645680010
-
Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions
-
A. Blanchet, J. Dolbeault, and B. Perthame, Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions, E. J. Diff. Eqn., 44, 1-32, 2006.
-
(2006)
E. J. Diff. Eqn.
, vol.44
, pp. 1-32
-
-
Blanchet, A.1
Dolbeault, J.2
Perthame, B.3
-
11
-
-
0034148193
-
Modeling the aggregative behavior of ants of the species polyergus rufescens
-
Spatial heterogeneity in ecological models (Alcalá de Henares, 1998)
-
S. Boi, V. Capasso, and D. Morale, Modeling the aggregative behavior of ants of the species polyergus rufescens, Nonlinear Anal. Real World Appl., 1(1), 163-176, 2000. Spatial heterogeneity in ecological models (Alcalá de Henares, 1998).
-
(2000)
Nonlinear Anal. Real World Appl.
, vol.1
, Issue.1
, pp. 163-176
-
-
Boi, S.1
Capasso, V.2
Morale, D.3
-
12
-
-
33746377577
-
Volume effects in the Keller-Segel model: Energy estimates preventing blow-up
-
V. Calvez and J.A. Carrillo, Volume effects in the Keller-Segel model: Energy estimates preventing blow-up, J. Math. Pures Appl., 86, 155-175, 2006.
-
(2006)
J. Math. Pures Appl.
, vol.86
, pp. 155-175
-
-
Calvez, V.1
Carrillo, J.A.2
-
13
-
-
79961233890
-
Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities
-
V. Calvez and J.A. Carrillo, Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities, arXiv:1007.2837v1, 2010.
-
(2010)
arXiv
, vol.1007
, pp. 28371
-
-
Calvez, V.1
Carrillo, J.A.2
-
15
-
-
18044401055
-
Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
-
J.A. Carrillo, A. Jüngel, P.A. Markowich, G. Toscani, and A. Unterreiter, Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, Montash. Math., 133, 1-82, 2001.
-
(2001)
Montash. Math.
, vol.133
, pp. 1-82
-
-
Carrillo, J.A.1
Jüngel, A.2
Markowich, P.A.3
Toscani, G.4
Unterreiter, A.5
-
16
-
-
1542399709
-
Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates
-
J.A. Carrillo, R.J. McCann, and C. Villani, Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates, Rev. Mat. Ibero., 19(3), 971-1018, 2003.
-
(2003)
Rev. Mat. Ibero.
, vol.19
, Issue.3
, pp. 971-1018
-
-
Carrillo, J.A.1
McCann, R.J.2
Villani, C.3
-
17
-
-
32544445429
-
Contractions in the 2-Wasserstein length space and thermalization of granular media
-
J.A. Carrillo, R.J. McCann, and C. Villani, Contractions in the 2-Wasserstein length space and thermalization of granular media, Arch. Rat. Mech. Anal., 179, 217-263, 2006.
-
(2006)
Arch. Rat. Mech. Anal.
, vol.179
, pp. 217-263
-
-
Carrillo, J.A.1
McCann, R.J.2
Villani, C.3
-
18
-
-
0032165708
-
Exponential convergence toward equilibrium for homogeneous Fokker-Plank-type equations
-
J.A. Carrillo and G. Toscani, Exponential convergence toward equilibrium for homogeneous Fokker-Plank-type equations, Math. Meth. Appl. Sci, 21, 1269-1286, 1998.
-
(1998)
Math. Meth. Appl. Sci
, vol.21
, pp. 1269-1286
-
-
Carrillo, J.A.1
Toscani, G.2
-
19
-
-
0003277699
-
1 decay of solutions of the porous medium equation to self-similarity
-
1 decay of solutions of the porous medium equation to self-similarity, Ind. Univ. Math. J., 49, 2000.
-
(2000)
Ind. Univ. Math. J
, vol.49
-
-
Carrillo, J.A.1
Toscani, G.2
-
20
-
-
26844499863
-
Global solutions of some chemotaxis and angiogenesis systems in high space dimensions
-
L. Corrias, B. Perthame, and H. Zaag, Global solutions of some chemotaxis and angiogenesis systems in high space dimensions, Milan J. Math., 72, 1-28, 2004.
-
(2004)
Milan J. Math.
, vol.72
, pp. 1-28
-
-
Corrias, L.1
Perthame, B.2
Zaag, H.3
-
21
-
-
0000489740
-
Information-type measures of difference of probability distributions and indirect observation
-
I. Csiszar, Information-type measures of difference of probability distributions and indirect observation, Stud. Sci. Math. Hung., 2, 299-318, 1967.
-
(1967)
Stud. Sci. Math. Hung.
, vol.2
, pp. 299-318
-
-
Csiszar, I.1
-
22
-
-
0001429116
-
Logrithmic Sobolev inequalities
-
L. Gross, Logrithmic Sobolev inequalities, Amer. J. Math., 97, 1061-1083, 1975.
-
(1975)
Amer. J. Math.
, vol.97
, pp. 1061-1083
-
-
Gross, L.1
-
23
-
-
0017357730
-
On the diffusion of biological populations
-
E.M. Gurtin and R.C McCamy, On the diffusion of biological populations, Math. Biosci., 33, 35-47, 1977.
-
(1977)
Math. Biosci.
, vol.33
, pp. 35-47
-
-
Gurtin, E.M.1
McCamy, R.C.2
-
24
-
-
63049107118
-
A user's guide to PDE models for chemotaxis
-
T. Hillen and K.J. Painter, A user's guide to PDE models for chemotaxis, J. Math. Biol., 58(1-2), 183-217, 2009.
-
(2009)
J. Math. Biol.
, vol.58
, Issue.1-2
, pp. 183-217
-
-
Hillen, T.1
Painter, K.J.2
-
25
-
-
4744373150
-
From 1970 until present: The Keller-Segel model in chemotaxis and its consequences, I
-
D. Horstmann, From 1970 until present: The Keller-Segel model in chemotaxis and its consequences, I, Jahresber. Deutsch. Math.-Verein, 105(3), 103-165, 2003.
-
(2003)
Jahresber. Deutsch. Math. -Verein
, vol.105
, Issue.3
, pp. 103-165
-
-
Horstmann, D.1
-
26
-
-
84966208077
-
On explosions of solutions to a system of partial differntial equations modelling chemotaxis
-
W. Jäger and S. Luckhaus, On explosions of solutions to a system of partial differntial equations modelling chemotaxis, Trans. Amer. Math. Soc., 329(2), 819-824, 1992.
-
(1992)
Trans. Amer. Math. Soc.
, vol.329
, Issue.2
, pp. 819-824
-
-
Jäger, W.1
Luckhaus, S.2
-
27
-
-
0000576544
-
Fundamental solutions and asymptotic behavior for the p-Laplacian equation
-
S. Kamin and J.L. Vázquez, Fundamental solutions and asymptotic behavior for the p-Laplacian equation, Ref. Mat. Iberoamericana, 4, 34-45, 1988.
-
(1988)
Ref. Mat. Iberoamericana
, vol.4
, pp. 34-45
-
-
Kamin, S.1
Vázquez, J.L.2
-
29
-
-
77952476338
-
Nonlinear Schr̈odinger equations at critical regularity
-
Clay summer school "Evolution Equations", to appear, June 23-July
-
R. Killip and M. Visan, Nonlinear Schr̈odinger equations at critical regularity, Proc. Clay summer school "Evolution Equations", to appear, June 23-July 18, 2008.
-
(2008)
Proc
, vol.18
-
-
Killip, R.1
Visan, M.2
-
30
-
-
79961219328
-
The Patlak-Keller-Segel model and its variations: Properties of solutions via maximum principle
-
I. Kim and Y. Yao, The Patlak-Keller-Segel model and its variations: Properties of solutions via maximum principle, arXiv, 1102.0092, 2011.
-
(2011)
arXiv
, pp. 1102-1192
-
-
Kim, I.1
Yao, Y.2
-
31
-
-
15844396394
-
Preventing blow-up in a chemotaxis model
-
R. Kowalczyk, Preventing blow-up in a chemotaxis model, J. Math. Anal. Appl., 305, 566-588, 2005.
-
(2005)
J. Math. Anal. Appl.
, vol.305
, pp. 566-588
-
-
Kowalczyk, R.1
-
32
-
-
84941465845
-
A lower bound for discrimination information in terms of variation
-
S. Kullback, A lower bound for discrimination information in terms of variation, IEEE Trans. Inf., 4, 126-127, 1967.
-
(1967)
IEEE Trans. Inf.
, vol.4
, pp. 126-127
-
-
Kullback, S.1
-
33
-
-
85030707196
-
The concentration-compactness principle in the calculus of variations the locally compact case
-
P.L. Lions, The concentration-compactness principle in the calculus of variations the locally compact case, Ann. I.H.P., Anal. Nonlin., 1(2), 109-145, 1984.
-
(1984)
Ann. I.H.P., Anal. Nonlin.
, vol.1
, Issue.2
, pp. 109-145
-
-
Lions, P.L.1
-
34
-
-
33746275846
-
Large time behavior of solutions in super-critical case to degenerate Keller-Segel systems
-
S. Luckhaus and Y. Sugiyama, Large time behavior of solutions in super-critical case to degenerate Keller-Segel systems, Math. Model. Numer. Anal., 40, 597-621, 2006.
-
(2006)
Math. Model. Numer. Anal.
, vol.40
, pp. 597-621
-
-
Luckhaus, S.1
Sugiyama, Y.2
-
35
-
-
34547452103
-
Asymptotic profile with optimal convergence rate for a parabolic equation of chemotaxis in super-critical cases
-
S. Luckhaus and Y. Sugiyama, Asymptotic profile with optimal convergence rate for a parabolic equation of chemotaxis in super-critical cases, Indiana Univ. Math. J., 56(3), 1279-1297, 2007.
-
(2007)
Indiana Univ. Math. J.
, vol.56
, Issue.3
, pp. 1279-1297
-
-
Luckhaus, S.1
Sugiyama, Y.2
-
36
-
-
0031161793
-
A convexity principle for interacting gases
-
R.J. McCann, A convexity principle for interacting gases, Adv. Math., 128, 153-179, 1997.
-
(1997)
Adv. Math.
, vol.128
, pp. 153-179
-
-
McCann, R.J.1
-
37
-
-
49349113659
-
A simple model for biological aggregation with asymmetric sensing
-
P.A. Milewski and X. Yang, A simple model for biological aggregation with asymmetric sensing, Commun. Math. Sci., 6(2), 397-416, 2008.
-
(2008)
Commun. Math. Sci.
, vol.6
, Issue.2
, pp. 397-416
-
-
Milewski, P.A.1
Yang, X.2
-
38
-
-
0005120141
-
A Lyapunov functional for the evolution to the porous medium equation to self-similarity
-
W.J. Newman, A Lyapunov functional for the evolution to the porous medium equation to self-similarity, J. Math. Phys., I, 25, 3120-3123, 1984.
-
(1984)
J. Math. Phys., I
, vol.25
, pp. 3120-3123
-
-
Newman, W.J.1
-
39
-
-
0001560970
-
-
F. Otto, The geometry of dissipative evolution equations: The porous medium equation, Commun. Part. Diff. Eqn., 26(1), 101-174, 2001.
-
(2001)
Commun. Part. Diff. Eqn.
, vol.26
, Issue.1
, pp. 101-174
-
-
Otto, F.1
-
40
-
-
51249193541
-
Random walk with persistence and external bias
-
C.S. Patlak, Random walk with persistence and external bias, Bull. Math. Biophys., 15, 311-338, 1953.
-
(1953)
Bull. Math. Biophys.
, vol.15
, pp. 311-338
-
-
Patlak, C.S.1
-
42
-
-
0036710614
-
Best constants for Galiardo-Nirenberg inequalities and applications to nonlinear diffusions
-
M. Del Pino and J. Dolbeault, Best constants for Galiardo-Nirenberg inequalities and applications to nonlinear diffusions, J. Math. Pures. Appl., 81, 847-875, 2002.
-
(2002)
J. Math. Pures. Appl.
, vol.81
, pp. 847-875
-
-
Del Pino, M.1
Dolbeault, J.2
-
43
-
-
0005170087
-
A Lyapunov functional for the evolution to the porous medium equation to selfsimilarity
-
J. Ralston, A Lyapunov functional for the evolution to the porous medium equation to selfsimilarity, J. Math. Phys., II, 25, 3124-3127, 1984.
-
(1984)
J. Math. Phys., II
, vol.25
, pp. 3124-3127
-
-
Ralston, J.1
-
44
-
-
0003279861
-
Harmonic Analysis: Real-Variable Methods
-
Princeton University Press
-
E. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, 1993.
-
(1993)
Orthogonality, and Oscillatory Integrals
-
-
Stein, E.1
-
45
-
-
34547418914
-
Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems
-
Y. Sugiyama, Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems, Diff. Int. Eqns., 19(8), 841-876, 2006.
-
(2006)
Diff. Int. Eqns.
, vol.19
, Issue.8
, pp. 841-876
-
-
Sugiyama, Y.1
-
46
-
-
43049127610
-
Application of the best constant of the Sobolev inequality to degenerate Keller-Segel models
-
Y. Sugiyama, Application of the best constant of the Sobolev inequality to degenerate Keller-Segel models, Adv. Diff. Eqns., 12(2), 121-144, 2007.
-
(2007)
Adv. Diff. Eqns.
, vol.12
, Issue.2
, pp. 121-144
-
-
Sugiyama, Y.1
-
47
-
-
34547463400
-
The global existence and asymptotic behavior of solutions to degenerate to quasilinear parabolic systems of chemotaxis
-
Y. Sugiyama, The global existence and asymptotic behavior of solutions to degenerate to quasilinear parabolic systems of chemotaxis, Diff. Int. Eqns., 20(2), 133-180, 2007.
-
(2007)
Diff. Int. Eqns.
, vol.20
, Issue.2
, pp. 133-180
-
-
Sugiyama, Y.1
-
48
-
-
33748692474
-
A nonlocal continuum model for biological aggregation
-
C.M. Topaz, A.L. Bertozzi, and M.A. Lewis, A nonlocal continuum model for biological aggregation, Bull. Math. Biol., 68(7), 1601-1623, 2006.
-
(2006)
Bull. Math. Biol.
, vol.68
, Issue.7
, pp. 1601-1623
-
-
Topaz, C.M.1
Bertozzi, A.L.2
Lewis, M.A.3
-
49
-
-
0032632377
-
Entropy production and the rate of convergence to equillibrium for the Fokker-Plank equation
-
G. Toscani, Entropy production and the rate of convergence to equillibrium for the Fokker-Plank equation, Quart. Appl. Math., 57, 521-541, 1999.
-
(1999)
Quart. Appl. Math.
, vol.57
, pp. 521-541
-
-
Toscani, G.1
|